Title: Rational $S^1$-equivariant stable homotopy theory.
Author: J.P.C.Greenlees
Abstract: We make a systematic study of rational $S^1$-equivariant
cohomology theories, or rather of their representing objects,
rational $S^1$-spectra.
In Part I we construct a complete algebraic model for the homotopy
category of $S^1$-spectra, reminiscent of the localization theorem.
The model is of homological dimension one, and
simple enough to allow practical calculations; in particular we obtain
a classification of rational $S^1$-equivariant cohomology theories.
The model for semifree spectra is the derived category of
the abelian category whose objects are $\Q [c]$-modules $N$
with a graded vector space $V$ giving an isomorphism
$N[c^{-1}] = \Q [c , c^{-1}] \tensor V$; the model for arbitrary
spectra is an appropriate generalization.
In Part II we identify the algebraic counterparts of all the usual $S^1$-spectra and constructions on $S^1$-spectra. This enables us
in Part III to give a rational analysis of a number of interesting
phenomena, such as the Atiyah-Hirzebruch spectral sequence, the Segal
conjecture, $K$-theory and topological cyclic cohomology.
For reasons of size this is broken into four parts
Part I (including Introduction and Table of Contents)
Part II
Part III
Appendices (including Conventions and Index).
Also available
The whole thing (s1q123.dvi)
Introduction and contents only (s1qIntro.dvi).